# Basic understanding of the motors torque and programming wit

Hi guys

I hope you have time to take a look at my calculation and tell me if this is possible to achieve.
I have to make a project, where I have to rotate an object which will resist more and more to the rotation. The protocol is:
Rotate the object with a torque of 5 Nm until the resistance becomes too large and the rotation will stop - now take a picture of the objects position.
Do the same thing with torques of 10, 15, 20, 25 Nm.
Since we have to do this approximately 1000 times, I would like it to be as automatized as possible.

I´m thinking it should not be a problem to program the motor through an Arduino Uno, but I'm not quite sure how I program the motor to stop at a specific torque.
I´m thinking to get 5 Nm of torque:
I found these two formulas:
1. Power (kw) = Torque (Nm) x Speed (RPM) / 9.5488
2. I (A) = Power(kw) x 1000 / (n x U) = , where n is the motors efficiency
I have not used motors before, but I believe you can adjust the speed (RPM) and the current applied to the motor through Arduino? Will the voltage be steady throughout the process, if I i.e. get at 12 V motor - or will it change? (Then my calculation won't work)

So if I want a torque of 5 Nm and I set the speed of 20 RPM can I then do this:

1. Power (kw) = 5 Nm x 20 RPM / 9.5488 = 0.01 kw.
2. I (A) = 0.01 kw x 1000 / (0.9 x 12 V) = 0.93 A
So, I´m thinking I can just program the motor to run at 20 RPM and gradually increase the current from 0 to 0.93 A, and when reaching 0.93 A the motor will stop for 5 seconds (to take the picture) and then rewind back to the starting position before starting over?

I guess there is a problem with the motors efficiency (n) and friction and perhaps other variables, but it is not the most important that the motor exactly performs 5 Nm or 4.8 Nm for that matter - the important thing is that is gives the same torque each time.

I hope you can clarify if I can do this, and your welcome to comment on obvious error or problems I can run into.

Kind regards
Kasper

jim hardy
Gold Member
Dearly Missed
I took my motors course back when sliderules were king, mid 1960's.

DC Electric motors external characteristics were described by these two equations which have served me well over the years:
Counter EMF = K X Φ X RPM , Φ being flux and proportional to excitation (field current)
Torque = 7.04 K X Φ X Iarmature
We determined the lumped constant K X Φ for any particular motor by spinning it at known RPM with known field excitation and measuring open circuit voltage,
volts/RPM = K X Φ at that flux

If you're using a small permanent magnet motor it'll have constant flux because of its permanent magnet field, so long as it's lightly loaded.
So you could get its K X Φ from open circuit voltage at known RPM.
Torque will be that same K X Φ multiplied first by 7.04 then by armature amps, so long as it's not heavily loaded.
so driving it with a constant current will cause it to rotate until it stalls, and stall torque will be set by armature amps.

Torque equation above gives torque in foot-pounds which is easy enough to convert to newton-meters..

My caveat about load on the motor is because of something called "Armature Reaction", which just means that high current in the armature distorts the internal flux distribution. So you'll want a motor capable of more torque than you're using.

So, there's an approach for you. Some experimentation will be required with the particular motor you select. Your project sounds about right for a junkyard Ford windshield wiper motor, one of my favorite tinkertoys. It is has a worm gear drive and can easily make the ~4 ft-lbs you want. Electric window motor is another possibility.

Experiment and have fun !

old jim

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